Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-7x+9y &= 9 \\ 8x+6y &= 6\end{align*}$
Answer: Begin by moving the $y$ -term in the second equation to the right side of the equation. $8x = -6y+6$ Divide both sides by $8$ to isolate $x$ $x = {-\dfrac{3}{4}y + \dfrac{3}{4}}$ Substitute this expression for $x$ in the first equation. $-7({-\dfrac{3}{4}y + \dfrac{3}{4}}) + 9y = 9$ $\dfrac{21}{4}y - \dfrac{21}{4} + 9y = 9$ Simplify by combining terms, then solve for $y$ $\dfrac{57}{4}y - \dfrac{21}{4} = 9$ $\dfrac{57}{4}y = \dfrac{57}{4}$ $y = 1$ Substitute $1$ for $y$ in the top equation. $-7x+9( 1) = 9$ $-7x+9 = 9$ $-7x = 0$ $x = 0$ The solution is $\enspace x = 0, \enspace y = 1$.